Question

The perimeter of a rectangle is 62m. find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Answer 1

The perimeter of a rectangle is 62m. find the length of its sides if it is known that the area of the rectangle is 1980000 cm².

Answer 2

Answer:

L=22 m or L=9 m

Step-by-step explanation:

We are given that

Perimeter of rectangle=62 m

Area of rectangle =$1980000cm^2=198m$ (1m=100 cm)

We have to find the lengths of its sides.

Let Length of rectangle =x

Breadth of rectangle=y

Perimeter of rectangle=2(x+y)

Area of rectangle =xy

According to question

$2(x+y)=62$

$x+y=\frac{62}{2}=31$

$xy=198$

$y=\frac{198}{x}$

Substitute the value of y

$x+\frac{198}{x}=31$

$\frac{x^2+198}{x}=31$

$x^2+198=31x$

$x^2-31x+198=0$

$x^2-22x-9x+198=0$

$x(x-22)-9(x-22)=0$

$(x-22)(x-9)=0$

$x-22=0\implies x=22$

$x-9\implies x=9$

Substitute the value x=22

$y=\frac{198}{22}=9$

Substitute the value of x=9

$y=\frac{198}{9}=22$

Hence, the length of sides of rectangle are

x=22 m and x=9 m